Anyon Superfluid in Trilayer Quantum Hall Systems.

Intertwining intrinsic topological order with gapless collective modes remains a central challenge in many-body physics. We show that a quantum-Hall trilayer at ν_{1}=ν_{2}=ν_{3}=1/3, tuned solely by the interlayer spacing d, realizes this goal. Large-scale density-matrix renormalization group calculations and a Chern-Simons field theory analysis reveal an intermediate "anyon-exciton condensate" separating the familiar ν_{tot}=1 exciton condensate (d→0) from three decoupled Laughlin liquids (d→∞). In this phase, neutral bi-excitons condense while a ν=2/3 Laughlin topological order survives, yielding a Goldstone mode coexisting with fractionalized anyons. A Ginzburg-Landau analysis maps out the finite-temperature phase diagram. The anyon-exciton condensate can be experimentally verified through a vanishing double-counter-flow resistance and a fractional layer-resolved Hall resistance of 5h/2e^{2}, both within reach of existing high-mobility trilayer devices.